Slope of a Line
Slope basically describes the
steepness of a line
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If a line goes up from left to right, then
the slope has to be positive
Conversely, if a line goes down from left
to right, then the slope has to be negative
Definitions of Slope
Slope is simply the change in the vertical
distance over the change in the
horizontal distance
rise y y2  y1
slope  m 


run x x2  x1
Read slope from a picture
y2  y1
m
x2  x1
The formula above is the one which we
will use to find the slope of specific lines
In order to use that formula we need to
know, or be able to find 2 points on the
line
Examples
 1,4 , 5,6 
64
m
5   1
2
1
m

6
3
Work Time
Find the slope of a line that contains points
A(-2, 5) B(4, -5)
If a line is in the form Ax + By = C, we
can use the following formula to find the
slope:
A
m
B
Example
2x  3y  5
2
m
3
-4x + 6y = 12
4 4 2

 
6
6 3
Horizontal lines have a slope of zero
while vertical lines have no slope
m=0
Vertical
Horizontal
m = no
slope
Examples of zero and no slope
A(5, -6) B(5, 3)
A(4,-2) B(1, -2)
Parallel and Perpendicular
Determine whether the lines are
parallel or perpendicular.
• [(-1, -8),(1,6)] and [(-2,-2),(2,10)]
• [(-1,4),(2,-5)] and [(-3,2),(3,0)]
• [(-4,-8),(4,-6)] and [(-3,5),(-1,-3)]
Graph the line with slope -¾ and
contains P(-3,3)
Graph the line that contains point
B(-4,2) and is parallel to line FG
with F(0,-3) and G(4,-2)
True or False
1. ALL HORIZONTAL LINES HAVE THE
SAME SLOPE
2. TWO LINES MAY HAVE THE SAME SLOPE
3. A LINE WITH A SLOPE OF 1
PASSES THROUGH THE ORIGIN
Lesson Summation
• Read slope from a picture
• Calculate slope from points
• ID lines as parallel or perpendicular from a
picture or points
• Graph lines from given conditions
• Understand slopes of vertical and horizontal